Percentages
X Out of Y as a Percentage
If you are asking what is a 15 out of 20, the answer is 75%. Every score out of a total follows one formula: divide the score by the total and multiply by 100. This guide gives the formula, a full lookup table, and the shortcuts.
X out of Y as a percentage: divide, then multiply by 100
A 15 out of 20 is 75%. A 26 out of 30 is 86.67%. A 20 out of 25 is 80%. Every one of those comes from the same two steps: divide the score by the total, then multiply the result by 100.
The division is the whole calculation. Multiplying by 100 is just a change of units: it moves the decimal point two places to the right so you can talk about the result in hundredths instead of in decimals. 15 ÷ 20 = 0.75, and 0.75 × 100 = 75%. The two numbers are the same quantity written two ways.
Order matters in the division. The score goes on top and the total goes on the bottom. Dividing 20 by 15 gives 1.333, which is not a test score. A quick sanity check: if you got less than everything available, the answer has to be under 100%. If it comes out above 100%, you divided the wrong way round.
Example: 26 out of 30
Divide first, then scale.
Thirty is not a factor of 100, so this one does not terminate. The digits repeat forever. Round at the end, not partway through, and quote it as 86.67% or simply 87%.
Example: 43 out of 60
Same two steps, larger numbers.
That lands in the C− band on the usual American scale. If you want to skip the arithmetic on any pair of numbers, the ratio to percentage calculator takes the two values and shows the division as well as the answer.
Every common test score as a percentage
Most classroom scores are out of 10, 20, 25 or 30, because those are the totals that divide cleanly into a quiz. Below is every possible score on each of those four totals, with the percentage, the fraction reduced to lowest terms, and the letter grade the percentage usually falls in.
Treat the letter column as the common case, not the rule. Cutoffs are set by the school or the instructor and they vary. Some schools start an A at 90 rather than 93, some do not use plus and minus at all, and some curve. The table uses the widely used ten-point scale with plus and minus: A from 93, A− from 90, B+ from 87, B from 83, B− from 80, C+ from 77, C from 73, C− from 70, D from 60, and F below that. Your syllabus is the authority.
Scores out of 10
| Score | Percentage | Fraction in lowest terms | Typical letter |
|---|---|---|---|
| 10 / 10 | 100% | 1 | A |
| 9 / 10 | 90% | 9/10 | A− |
| 8 / 10 | 80% | 4/5 | B− |
| 7 / 10 | 70% | 7/10 | C− |
| 6 / 10 | 60% | 3/5 | D |
| 5 / 10 | 50% | 1/2 | F |
| 4 / 10 | 40% | 2/5 | F |
| 3 / 10 | 30% | 3/10 | F |
| 2 / 10 | 20% | 1/5 | F |
| 1 / 10 | 10% | 1/10 | F |
| 0 / 10 | 0% | 0 | F |
Scores out of 20
| Score | Percentage | Fraction in lowest terms | Typical letter |
|---|---|---|---|
| 20 / 20 | 100% | 1 | A |
| 19 / 20 | 95% | 19/20 | A |
| 18 / 20 | 90% | 9/10 | A− |
| 17 / 20 | 85% | 17/20 | B |
| 16 / 20 | 80% | 4/5 | B− |
| 15 / 20 | 75% | 3/4 | C |
| 14 / 20 | 70% | 7/10 | C− |
| 13 / 20 | 65% | 13/20 | D |
| 12 / 20 | 60% | 3/5 | D |
| 11 / 20 | 55% | 11/20 | F |
| 10 / 20 | 50% | 1/2 | F |
| 9 / 20 | 45% | 9/20 | F |
| 8 / 20 | 40% | 2/5 | F |
| 7 / 20 | 35% | 7/20 | F |
| 6 / 20 | 30% | 3/10 | F |
| 5 / 20 | 25% | 1/4 | F |
| 4 / 20 | 20% | 1/5 | F |
| 3 / 20 | 15% | 3/20 | F |
| 2 / 20 | 10% | 1/10 | F |
| 1 / 20 | 5% | 1/20 | F |
| 0 / 20 | 0% | 0 | F |
Scores out of 25
| Score | Percentage | Fraction in lowest terms | Typical letter |
|---|---|---|---|
| 25 / 25 | 100% | 1 | A |
| 24 / 25 | 96% | 24/25 | A |
| 23 / 25 | 92% | 23/25 | A− |
| 22 / 25 | 88% | 22/25 | B+ |
| 21 / 25 | 84% | 21/25 | B |
| 20 / 25 | 80% | 4/5 | B− |
| 19 / 25 | 76% | 19/25 | C |
| 18 / 25 | 72% | 18/25 | C− |
| 17 / 25 | 68% | 17/25 | D |
| 16 / 25 | 64% | 16/25 | D |
| 15 / 25 | 60% | 3/5 | D |
| 14 / 25 | 56% | 14/25 | F |
| 13 / 25 | 52% | 13/25 | F |
| 12 / 25 | 48% | 12/25 | F |
| 11 / 25 | 44% | 11/25 | F |
| 10 / 25 | 40% | 2/5 | F |
| 9 / 25 | 36% | 9/25 | F |
| 8 / 25 | 32% | 8/25 | F |
| 7 / 25 | 28% | 7/25 | F |
| 6 / 25 | 24% | 6/25 | F |
| 5 / 25 | 20% | 1/5 | F |
| 4 / 25 | 16% | 4/25 | F |
| 3 / 25 | 12% | 3/25 | F |
| 2 / 25 | 8% | 2/25 | F |
| 1 / 25 | 4% | 1/25 | F |
| 0 / 25 | 0% | 0 | F |
Scores out of 30
| Score | Percentage | Fraction in lowest terms | Typical letter |
|---|---|---|---|
| 30 / 30 | 100% | 1 | A |
| 29 / 30 | 96.67% | 29/30 | A |
| 28 / 30 | 93.33% | 14/15 | A |
| 27 / 30 | 90% | 9/10 | A− |
| 26 / 30 | 86.67% | 13/15 | B |
| 25 / 30 | 83.33% | 5/6 | B |
| 24 / 30 | 80% | 4/5 | B− |
| 23 / 30 | 76.67% | 23/30 | C |
| 22 / 30 | 73.33% | 11/15 | C |
| 21 / 30 | 70% | 7/10 | C− |
| 20 / 30 | 66.67% | 2/3 | D |
| 19 / 30 | 63.33% | 19/30 | D |
| 18 / 30 | 60% | 3/5 | D |
| 17 / 30 | 56.67% | 17/30 | F |
| 16 / 30 | 53.33% | 8/15 | F |
| 15 / 30 | 50% | 1/2 | F |
| 14 / 30 | 46.67% | 7/15 | F |
| 13 / 30 | 43.33% | 13/30 | F |
| 12 / 30 | 40% | 2/5 | F |
| 11 / 30 | 36.67% | 11/30 | F |
| 10 / 30 | 33.33% | 1/3 | F |
| 9 / 30 | 30% | 3/10 | F |
| 8 / 30 | 26.67% | 4/15 | F |
| 7 / 30 | 23.33% | 7/30 | F |
| 6 / 30 | 20% | 1/5 | F |
| 5 / 30 | 16.67% | 1/6 | F |
| 4 / 30 | 13.33% | 2/15 | F |
| 3 / 30 | 10% | 1/10 | F |
| 2 / 30 | 6.67% | 1/15 | F |
| 1 / 30 | 3.33% | 1/30 | F |
| 0 / 30 | 0% | 0 | F |
Notice how the out-of-30 column behaves differently from the other three. Ten, 20 and 25 all divide into 100, so every score gives a percentage that ends after at most one decimal place. Thirty does not, so two thirds of the rows repeat forever and have to be rounded. That is why a 26 out of 30 gets written as 86.67% rather than as something tidy.
Shortcuts for totals that divide into 100
When the total divides evenly into 100, you do not need to divide at all. You just multiply the score by a fixed number. This works because score ÷ total × 100 can be rearranged as score × (100 ÷ total), and when 100 ÷ total is a whole number the multiplication is easy.
| Out of | Multiply the score by | Why | Example |
|---|---|---|---|
| 2 | 50 | 100 ÷ 2 = 50 | 1 out of 2 = 50% |
| 4 | 25 | 100 ÷ 4 = 25 | 3 out of 4 = 75% |
| 5 | 20 | 100 ÷ 5 = 20 | 4 out of 5 = 80% |
| 10 | 10 | 100 ÷ 10 = 10 | 7 out of 10 = 70% |
| 20 | 5 | 100 ÷ 20 = 5 | 15 out of 20 = 75% |
| 25 | 4 | 100 ÷ 25 = 4 | 20 out of 25 = 80% |
| 50 | 2 | 100 ÷ 50 = 2 | 47 out of 50 = 94% |
| 100 | 1 | 100 ÷ 100 = 1 | 88 out of 100 = 88% |
Out of 20 is the one worth memorizing, because it comes up constantly. Multiply by five. A 17 out of 20 is 85%. A 13 out of 20 is 65%. If multiplying by five feels awkward, double the score and move the decimal one place: 17 doubled is 34, so 17 out of 20 is 85%.
Out of 25, multiply by four, which is two doublings. A 19 out of 25 is 38, then 76%. Out of 50, just double: 43 out of 50 is 86%.
Totals that do not divide into 100
For 30, 40, 60, 80 and anything irregular, the useful move is to find one mark first. On a 30-point test, one mark is 100 ÷ 30 = 3.333%. So 26 marks is 26 × 3.333 = 86.67%, and every extra point is worth about three and a third percent. On a 40-point test, one mark is 2.5%, which is exact and easy: 33 out of 40 is 33 × 2.5 = 82.5%.
Going backwards: what is X percent of Y
The reverse question comes up whenever a target is set as a percentage and you need to know how many marks that is. It is the same equation rearranged.
What is 85% of 40? Divide 85 by 100 to get 0.85, then multiply: 0.85 × 40 = 34. You need 34 marks out of 40. What is 15% of 80? 0.15 × 80 = 12. What is 72% of 25? 0.72 × 25 = 18.
Example: how many marks do you need for a B?
The test is out of 45 and a B starts at 83%.
You cannot score 37.35 marks, so you need 38. Always round up when the answer is a threshold you have to clear. Thirty-seven marks would be 37 ÷ 45 = 82.22%, which lands in the B− band instead.
That rounding rule catches people out. When you are computing what you scored, round normally. When you are computing what you need, round up to the next whole mark, because partial marks are usually not awarded and being one hundredth of a percent short still means missing the cutoff.
Averaging several scores
If you have several tests with the same total, convert each to a percentage and take the mean of the percentages, or add all the scores and divide by all the totals. Both give the same answer when the totals match. On a set of three tests scored 15/20, 17/20 and 12/20, the percentages are 75%, 85% and 60%, and their mean is 220 ÷ 3 = 73.33%. Adding raw scores gives 44 ÷ 60, which is also 73.33%. The average calculator will do the mean for you.
When the totals differ, the two methods do not agree, and the raw-score method is the one that reflects reality. That gap is the difference between a mean and a weighted mean, and it is covered in the guide on how to calculate your final grade.
How to turn a percent into a fraction
A percentage is already a fraction. The word means “per hundred”, so 75% literally means 75 out of 100. To write it as a fraction, put the number over 100 and reduce.
Take 75%. Write it as 75/100. The largest number that divides both 75 and 100 is 25. Divide top and bottom by 25 and you get 3/4. That is why a 15 out of 20 and a 3 out of 4 are the same score: both are 75%.
Example: 88% as a fraction
Check it back: 22 ÷ 25 = 0.88, which is 88%.
Percentages with decimals in them
If the percentage has a decimal, multiply top and bottom until the top is a whole number, then reduce. For 62.5%, write 62.5/100, multiply both by 10 to get 625/1000, and reduce by 125 to get 5/8.
Repeating percentages like 86.67% are a special case. That figure is a rounded version of 86.666…%, which came from 26/30. If you reduce the rounded number you get 8667/10000, which does not simplify and is not the fraction you wanted. When the percentage repeats, go back to the original score. 26/30 reduces to 13/15, because 26 and 30 share a factor of 2.
How to convert a decimal to a percent and back
This is the shortest conversion in arithmetic and it goes both ways.
0.75 becomes 75%. 0.4 becomes 40%. 0.06 becomes 6%. 1.25 becomes 125%, which is perfectly legitimate for things like growth rates even though it cannot happen on a normal test. Going the other way, 8% becomes 0.08, 92% becomes 0.92, and 3.5% becomes 0.035.
| Decimal | Percent | Fraction |
|---|---|---|
| 0.01 | 1% | 1/100 |
| 0.05 | 5% | 1/20 |
| 0.1 | 10% | 1/10 |
| 0.125 | 12.5% | 1/8 |
| 0.2 | 20% | 1/5 |
| 0.25 | 25% | 1/4 |
| 0.333… | 33.33% | 1/3 |
| 0.375 | 37.5% | 3/8 |
| 0.5 | 50% | 1/2 |
| 0.6 | 60% | 3/5 |
| 0.625 | 62.5% | 5/8 |
| 0.666… | 66.67% | 2/3 |
| 0.75 | 75% | 3/4 |
| 0.8 | 80% | 4/5 |
| 0.875 | 87.5% | 7/8 |
| 0.9 | 90% | 9/10 |
| 1 | 100% | 1 |
The mistake here is dropping a zero. 0.05 is 5%, not 50%. Count the places rather than eyeballing it: the decimal point in 0.05 moves past the 0 and then past the 5, landing after the 5, which reads as 5. If you would rather have the conversion done for you in either direction, use the decimal to percent calculator or the percent to decimal calculator.
Common mistakes
- Dividing the total by the score. 20 ÷ 15 = 1.33, not 0.75. The score you earned always goes on top.
- Forgetting the × 100. 15 ÷ 20 = 0.75. Reporting that as “0.75%” is off by a factor of 100.
- Rounding partway through. Carry the full decimal until the last step. Rounding 26 ÷ 30 to 0.87 and then multiplying gives 87%, which is close but not what the arithmetic says.
- Assuming the letter grade. A 75% is a C on the common ten-point scale, but plenty of schools set different cutoffs, and some courses are curved. Check the syllabus.
- Averaging percentages from tests with different totals. A 9/10 and a 45/90 are not equally weighted evidence. Add the points, or use a weighted mean.
- Rounding down when you need a threshold. If 83% of 45 is 37.35 marks, you need 38, not 37.
- Reducing a fraction from a rounded percentage. 86.67% is not 8667/10000 in any useful sense. It is 13/15.
- Mixing up “15 out of 20” with “15% of 20”. The first is 75%. The second is 3.
Frequently asked questions
What is a 15 out of 20 as a percentage?
A 15 out of 20 is 75%. Divide 15 by 20 to get 0.75, then multiply by 100. The shortcut for anything out of 20 is to multiply the score by 5, since 15 × 5 = 75. On the common ten-point scale that is a C. As a fraction in lowest terms, 15/20 reduces to 3/4.
What is a 26 out of 30 as a percentage?
A 26 out of 30 is 86.67%. The division is 26 ÷ 30 = 0.86666…, which repeats, so it gets rounded to two decimal places. That normally lands in the B band. If you need the exact fraction, 26/30 reduces to 13/15 — do not try to reduce the rounded percentage.
What is a 20 out of 25 as a percentage?
A 20 out of 25 is 80%. Because 25 divides into 100 exactly four times, you can multiply the score by 4 instead of dividing: 20 × 4 = 80. On the usual scale 80% is a B−, sitting right on the cutoff. In lowest terms, 20/25 is 4/5.
What is a 17 out of 20 as a percentage?
A 17 out of 20 is 85%. Multiply by 5: 17 × 5 = 85. If multiplying by 5 is awkward, double the score to 34 and move the decimal point one place left. That gives 3.4, then scale by 10 for 85%. Eighty-five percent is usually a B.
How do you calculate a percentage out of any total?
Divide the score by the total, then multiply by 100. That is the whole method: score ÷ total × 100. For 34 out of 45, 34 ÷ 45 = 0.7556, so the score is 75.56%. The ratio to percentage calculator shows the division and the result for any pair of numbers.
What is 15 percent of 80?
It is 12. Convert 15% to the decimal 0.15, then multiply by 80: 0.15 × 80 = 12. In your head, 10% of 80 is 8 and half of that is 4, so 15% is 8 + 4 = 12. Note this is a different question from “15 out of 80”, which is 18.75%.
How do you turn a percent into a fraction?
Write the percentage over 100, then reduce. 40% becomes 40/100, and dividing top and bottom by 20 gives 2/5. For 62.5%, first clear the decimal: 62.5/100 becomes 625/1000, which reduces to 5/8. If the percentage repeats, go back to the original numbers instead of reducing the rounded figure.
How do you convert a decimal to a percent?
Multiply by 100, which moves the decimal point two places right. 0.42 becomes 42%, 0.7 becomes 70%, and 0.035 becomes 3.5%. To go the other way, divide by 100 and move the point two places left. The percent to decimal calculator handles the reverse direction.
What score do I need out of 40 to get 90%?
You need 36. Convert 90% to 0.90 and multiply by the total: 0.90 × 40 = 36. Because 40 does not divide into 100 evenly, targets on a 40-point test often land between marks. When that happens, round up — 35.5 marks means you need 36 to clear the cutoff.
Is 75% a good grade?
On the common American ten-point scale, 75% is a C, which is a passing grade in most courses. Cutoffs vary by school, though. Some institutions place a C at 70–79 with no plus or minus, some require a C or better for major requirements, and graduate programs often set a higher floor. Check the syllabus for the course.
Calculators for this
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More guides
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